Page 171 - Electrical Properties of Materials

Preparation of pure and controlled-impurity single-crystal semiconductors 153

(a) Heating coil
Furnace wall

Travel

B t a o M o z n e t l o e n

Temperature
Melting point
Fig. 8.23
Zone refining. The molten zone
moving through the crystal sweeps
(b) Distance the impurities to the far end.

melt a slice of it, and arrange for the molten zone to travel along the crystal
length. This can be done by putting it in a refractory boat and dragging it slowly
through a furnace, as shown in Fig. 8.23. At any point, the solid separating out
at the back of the zone will be k times as impure as the melted material which,
as k < 1, is an improvement. By a fairly simple piece of algebra it can be
shown that the impurity concentration in the solid, C s (x), after the zone has
passed down the crystal (of length l ) once is
Since k is typically 0.1, it is pos-
sible to drive most of the impurity
C s (x)= C 0 {1 –(1– k)exp(–kx/z)}, (8.66)
to a small volume at the far end
with relatively few passes.
where C 0 is the initial concentration and z is the length of the molten zone.
Clearly, at the end of the crystal that is melted first, the value of impurity
concentration will be

n
C s (0) = k C 0 (8.67)
Rotating
if this process is repeated n times. chuck
This very simple idea is the basis of the great success of semiconductor en-
Floating zone
gineering. As we have said before impurities can be reduced to a few parts in
10
10 , and then they are usually limited by impurities picked up from reactions
with the boat. This latter problem showed up rather strongly when the semicon- Heating coil
ductor industry went over from germanium (melting point 937 C) to silicon
◦
(melting point 1958 C). The solution was the floating zone method, which dis-
◦
Silica envelope
pensed with the boat altogether. In this method the crystal is held vertically in containing inert
a rotating chuck (Fig. 8.24). It is surrounded at a reasonable distance by a cool atmosphere
silica envelope, so that it can be kept in an inert atmosphere, then outside this Crystal
is a single-turn coil of water-cooled copper tubing. A large high-frequency cur-
rent (several MHz) is passed through the coil, and the silicon crystal is heated Fig. 8.24
to melting point by the eddy currents induced in it. The coil is slowly moved up Floating zone refining.